{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7XENTMPLZTWF7GPW2ZTEF56ZZ7","short_pith_number":"pith:7XENTMPL","canonical_record":{"source":{"id":"1410.1001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-04T00:24:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a4e03af0bce698e88bf907307163eddda70ddc1ee30800e38a522790defd255","abstract_canon_sha256":"a1324273e24528c05dfa5b72acfa4250e9121c2090e4e7f29e8632ca7d39ae2c"},"schema_version":"1.0"},"canonical_sha256":"fdc8d9b1ebccec5f99f6d66642f7d9cfdaee991d45e95c425b05361f5a39797c","source":{"kind":"arxiv","id":"1410.1001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1001","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1001v2","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1001","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"7XENTMPLZTWF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7XENTMPLZTWF7GPW","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7XENTMPL","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7XENTMPLZTWF7GPW2ZTEF56ZZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-04T00:24:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a4e03af0bce698e88bf907307163eddda70ddc1ee30800e38a522790defd255","abstract_canon_sha256":"a1324273e24528c05dfa5b72acfa4250e9121c2090e4e7f29e8632ca7d39ae2c"},"schema_version":"1.0"},"canonical_sha256":"fdc8d9b1ebccec5f99f6d66642f7d9cfdaee991d45e95c425b05361f5a39797c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:55.293629Z","signature_b64":"JdEpZ9o4JWlBsOh0ShE09JI2M2kt3Wqj/6WKkhj0jWclQzHOfN4JXM/Dp5KfIdvgOPtd5P3Uf6VnOaDGsvCFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdc8d9b1ebccec5f99f6d66642f7d9cfdaee991d45e95c425b05361f5a39797c","last_reissued_at":"2026-05-18T02:40:55.293136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:55.293136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1001","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42ogBKrQNTvJXjbd4lz0l+ijxhhzEf9LoOyDGALn+gQypbTdku6N0RXdj4mzQmLP2F0xJZ+M2wqrZbUYbQC9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:11:00.121008Z"},"content_sha256":"efaae20751d08020b34b3f5b0d7d809eaf542a01d146d141030f8fef1405fff1","schema_version":"1.0","event_id":"sha256:efaae20751d08020b34b3f5b0d7d809eaf542a01d146d141030f8fef1405fff1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7XENTMPLZTWF7GPW2ZTEF56ZZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic differential operators on a semistable model of ${\\mathbb P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Deepam Patel, Matthias Strauch, Tobias Schmidt","submitted_at":"2014-10-04T00:24:00Z","abstract_excerpt":"In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves is non-torsion. We also consider a refinement of the order filtration on the sheaf of level zero (before taking the p-adic completion). The associated graded sheaf, which we explicitly determine, explains to some extent the occurrence of the cohomology classes in degree one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1001","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lW1DaW8moUhRU07m09DRa7r6sTcaC72EdsU2bd4Cjlc8HVhoyjqyHmYomGLmDvjSpjoHF+qAmfXYE9En9kzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:11:00.121383Z"},"content_sha256":"a0dd9fa8d57bb77267c26ff4d47496d4a723ce2caba0e7457f7d2e0986fa3440","schema_version":"1.0","event_id":"sha256:a0dd9fa8d57bb77267c26ff4d47496d4a723ce2caba0e7457f7d2e0986fa3440"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/bundle.json","state_url":"https://pith.science/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T21:11:00Z","links":{"resolver":"https://pith.science/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7","bundle":"https://pith.science/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/bundle.json","state":"https://pith.science/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XENTMPLZTWF7GPW2ZTEF56ZZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7XENTMPLZTWF7GPW2ZTEF56ZZ7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a1324273e24528c05dfa5b72acfa4250e9121c2090e4e7f29e8632ca7d39ae2c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-04T00:24:00Z","title_canon_sha256":"7a4e03af0bce698e88bf907307163eddda70ddc1ee30800e38a522790defd255"},"schema_version":"1.0","source":{"id":"1410.1001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1001","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1001v2","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1001","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"7XENTMPLZTWF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7XENTMPLZTWF7GPW","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7XENTMPL","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:a0dd9fa8d57bb77267c26ff4d47496d4a723ce2caba0e7457f7d2e0986fa3440","target":"graph","created_at":"2026-05-18T02:40:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves is non-torsion. We also consider a refinement of the order filtration on the sheaf of level zero (before taking the p-adic completion). The associated graded sheaf, which we explicitly determine, explains to some extent the occurrence of the cohomology classes in degree one.","authors_text":"Deepam Patel, Matthias Strauch, Tobias Schmidt","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-04T00:24:00Z","title":"Arithmetic differential operators on a semistable model of ${\\mathbb P}^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1001","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:efaae20751d08020b34b3f5b0d7d809eaf542a01d146d141030f8fef1405fff1","target":"record","created_at":"2026-05-18T02:40:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a1324273e24528c05dfa5b72acfa4250e9121c2090e4e7f29e8632ca7d39ae2c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-04T00:24:00Z","title_canon_sha256":"7a4e03af0bce698e88bf907307163eddda70ddc1ee30800e38a522790defd255"},"schema_version":"1.0","source":{"id":"1410.1001","kind":"arxiv","version":2}},"canonical_sha256":"fdc8d9b1ebccec5f99f6d66642f7d9cfdaee991d45e95c425b05361f5a39797c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdc8d9b1ebccec5f99f6d66642f7d9cfdaee991d45e95c425b05361f5a39797c","first_computed_at":"2026-05-18T02:40:55.293136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:55.293136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JdEpZ9o4JWlBsOh0ShE09JI2M2kt3Wqj/6WKkhj0jWclQzHOfN4JXM/Dp5KfIdvgOPtd5P3Uf6VnOaDGsvCFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:55.293629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efaae20751d08020b34b3f5b0d7d809eaf542a01d146d141030f8fef1405fff1","sha256:a0dd9fa8d57bb77267c26ff4d47496d4a723ce2caba0e7457f7d2e0986fa3440"],"state_sha256":"f41258c7f31deb697b0c71402b45392556d3d3c57d1bc324fb94f53e07464b84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZwJ4W6Km0kQUGvLU0k3e14U+EkhVjYbMsHEnNp/pHk59d0thNpIbP2DupSYgODXDHqCF5TElS9p54WKLu5ADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:11:00.124485Z","bundle_sha256":"236117eccf4a79b6a65b6020cc0ed641b9b8c3d782e2af2f05fe18520f3cb3f9"}}